Collapses and Watersheds in Pseudomanifolds

  • Authors:

  • Jean Cousty;Gilles Bertrand;Michel Couprie;Laurent Najman

  • Affiliations:

  • Laboratoire d'Informatique Gaspard-Monge, A3SI,ESIEE, Université Paris-Est,;Laboratoire d'Informatique Gaspard-Monge, A3SI,ESIEE, Université Paris-Est,;Laboratoire d'Informatique Gaspard-Monge, A3SI,ESIEE, Université Paris-Est,;Laboratoire d'Informatique Gaspard-Monge, A3SI,ESIEE, Université Paris-Est,

  • Venue:
  • IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
  • Year:
  • 2009

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Abstract

This work is settled in the framework of abstract simplicial complexes. We propose a definition of a watershed and of a collapse for maps defined on pseudomanifolds of arbitrary dimension. Through an equivalence theorem, we establish a deep link between these two notions: any watershed can be obtained by collapse iterated until idempotence, and conversely any collapse iterated until idempotence induces a watershed. We also state an equivalence result which links the notions of a watershed and of a collapse with the one of a minimum spanning forest.